Question

PLEASEEEE HELPPPPP
* MEDAL WILL BE AWARDED
In the diagram below, the length of the legs and of right triangle ABC are 6 cm and 8 cm, respectively. Altitude is drawn to the hypotenuse ofΔABC.
http://www.castlelearning.com/review/Courses/geometry/q4416.gif?v=20090930102956

1)3.6
2)6.0
3)6.4
4)4.0

Answer 1

A) 3.6

Answer 2

I don't need to show work correct?

Answer 3

If you actually wanted to know to do such a problem, read on.

We have a right triangle with sides 6 and 8 and hypotenuse AB. We can find the hypotenuse using Pythagorean theorem: \[{AB}^2 = 6^2 + 8^2\]\[{AB}^2=100\]\[AB=10\]

Now we have two similar triangles (we can flip one into the other without changing the angles). AD (aka x) corresponds to AC, BC corresponds to DC, and AB corresponds to AC. We know that AC = 6, BC = 8, and now AB = 10. Because the triangles are similar, the corresponding sides will be proportional. In particular, the ratio of hypotenuse AC of the little triangle to hypotenuse AB of the big triangle will be the same as the ratio of side AD to AC. In other words, 10:6 = 6:x.